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Positivity and stability for cauchy problems with delay

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Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1324))

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References

  1. Amann, H.: Gewöhnliche Differentialgleichungen, Berlin-New York, de Gruyter 1983.

    Google Scholar 

  2. Becker, I., Greiner, G.: On the Modulus of One-parameter Semigroups. Semigroup Forum (to appear).

    Google Scholar 

  3. Bell, G.I., Glasstone, S.: Nuclear Reactor Theory, p. 463. New York, Van Nostrand 1970.

    Google Scholar 

  4. Capasso, V., Maddalena, L.: Convergence to Equilibrium States for a Reaction-Diffusion System Modelling the Spatial Spread of a Class of Bacterial and Viral Diseases. J. Math. Biol. 13 (1981), 173–184.

    Article  MathSciNet  MATH  Google Scholar 

  5. Cooke, K.L., Ferreira, J.M.: Stability Conditions for Linear Retarded Functional Differential Equations. J. Math. Anal. Appl. 96 (1983), 480–504.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cushing, J.M.: Integrodifferential Equations and Delay Models in Population Dynamics. Lecture Notes in Biomathematics 20, Berlin, Springer-Verlag 1977.

    MATH  Google Scholar 

  7. Datko, R.: A Procedure for Determination of the Exponential Stability of Certain Differential Difference Equations. Quart. Appl. Math. 36 (1978), 279–292.

    MathSciNet  MATH  Google Scholar 

  8. Derndinger, R.: Betragshalbgruppen normstetiger Operatorenhalbgruppen. Arch. Math. 42 (1984), 371–375.

    Article  MathSciNet  MATH  Google Scholar 

  9. Di Blasio, G., Kunisch, K., Sinestrari, E.: Stability for Abstract Linear Functional Differential Equations. Israel J. Math. 50 (1985), 231–263.

    Article  MathSciNet  MATH  Google Scholar 

  10. Dickerson, J., Gibson, J.: Stability of Linear Functional Differential Equations on Banach Spaces. J. Math. Anal. Appl. 55 (1976), 150–155.

    Article  MathSciNet  MATH  Google Scholar 

  11. Goldstein, J.A.: Semigroups of Linear Operators and Applications. Oxford University Press 1985.

    Google Scholar 

  12. Goodwin, B.C.: Temporal Organization in Cells. New York, Academic Press 1963.

    Google Scholar 

  13. Grabosch, A., Moustakas, U.: A Semigroup Approach to Retarded Differential Equations in C([−1,0]). Section B-IV in [29].

    Google Scholar 

  14. Green, D., Stech, H.W.: Diffusion and Hereditary Effects in a Class Population Models. In: Differential Equations and Applications, Academic Press 1981.

    Google Scholar 

  15. Greiner, G.: Perturbing the Boundary Condition of a Generator. To appear in Houston J. Math..

    Google Scholar 

  16. Greiner, G.: Spectral Properties and Asymptotic Behaviour of the Linear Transport Equation. Math. Z. 185 (1984), 167–177.

    Article  MathSciNet  MATH  Google Scholar 

  17. Hadeler, H.P.: Delay Equations in Biology. In: Peitgen, H.O., Walther, H.O. (eds.): Functional Differential Equations and Approximations of Fixed Points. Lecture Notes Math. 730, Springer Verlag 1979.

    Google Scholar 

  18. Hale, J.K.: Functional Differential Equations. New York-Berlin, Springer Verlag 1977

    Book  MATH  Google Scholar 

  19. Hale, J.K., Infante, E.F., Tsen, F.P.: Stability in Linear Delay Equations. J. Math. Anal. Appl. 105 (1985), 533–555.

    Article  MathSciNet  MATH  Google Scholar 

  20. Infante, E.F.: A Note of Stability in Retarded Delay Systems for all Delays. In: Dynamical Systems II, edited by A. Bednarek and L. Cesari, 121–133, New York, Academic Press 1982.

    Google Scholar 

  21. Kaper, H.G., Lekkerkerker, C.G., Hejtmanek, J.: Spectral Methods in Linear Transport Theory. Basel, Birkhäuser Verlag 1982.

    MATH  Google Scholar 

  22. Kerscher W.: Majorisierung und Stabilität der Lösungen retardierter Cauchyprobleme. Dissertation, Tübingen 1986.

    Google Scholar 

  23. Kerscher W., Nagel, R.: Asymptotic Behavior of One-parameter Semigroups of Positive Operators. Acta Appl. Math. 2 (1984), 297–309.

    Article  MathSciNet  MATH  Google Scholar 

  24. Kunisch, K., Schappacher, W.: Necessary Conditions for Partial Differential Equations with Delay to generate Co-Semigroups. J. Diff. Equations 50 (1983), 49–79.

    Article  MathSciNet  MATH  Google Scholar 

  25. Landahl, H.D.: Some Conditions of Sustained Oscillations in Biochemical Chains with Feedback Inhibition. Bull. Math. Biophysics 31 (1969), 775–787.

    Article  MATH  Google Scholar 

  26. Lenhart, S.M., Travis, C.C.: Stability of Functional Partial Differential Equations. J. Diff. Equations 58 (1985), 212–227.

    Article  MathSciNet  MATH  Google Scholar 

  27. Lenhart, S.M., Travis, C.C.: Global Stability of a Biological Model with Time Delay. Proc. Amer. Math. Soc. 96 (1986), 75–78.

    Article  MathSciNet  MATH  Google Scholar 

  28. MacDonald, N.: Time Lag in a Model of a Biochemical Reaction Sequence with End Product Inhibition. J. theoret. Biol. 67 (1977), 549–556.

    Article  MathSciNet  Google Scholar 

  29. Nagel, R. (editor): One-parameter Semigroups of Positive Operators. Lecture Notes Math. 1184, Springer-Verlag 1986.

    Google Scholar 

  30. Nagel, R.: What can Positivity do for Stability? In: Functional Analysis, Surveys and Results III, 145–154, North Holland 1984.

    Google Scholar 

  31. Phillips, R.S.: Perturbation Theory for Semigroups of Linear Operators. Trans. Amer. Math. Soc. 74 (1953), 199–221.

    Article  MathSciNet  Google Scholar 

  32. Schaefer, H.H.: Banach Lattices and Positive Operators. Berlin, Springer Verlag 1974.

    Book  MATH  Google Scholar 

  33. Stech, H.W.: The Effect of Time Lags on the Stability of the Equilibrium State of Population Growth Equations. J. Math. Biology 5 (1978), 115–120.

    Article  MathSciNet  MATH  Google Scholar 

  34. Travis, C., Webb, G.: Existence and Stability for Partial Functional Differential Equations. Trans Amer. Math. Soc. 200 (1974), 395–418.

    Article  MathSciNet  MATH  Google Scholar 

  35. Voigt, J.: Positivity in Time Dependent Linear Transport Theory. Acta Appl. Math. 2 (1984), 311–331.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Auf der Morgenstelle 10, D-7400, Tübingen

    Wolfgang Kerscher & Rainer Nagel

Authors
  1. Wolfgang Kerscher
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  2. Rainer Nagel
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Editor information

Fernando Cardoso Djairo G. de Figueiredo Rafael Iório Orlando Lopes

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© 1988 Springer-Verlag

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Kerscher, W., Nagel, R. (1988). Positivity and stability for cauchy problems with delay. In: Cardoso, F., de Figueiredo, D.G., Iório, R., Lopes, O. (eds) Partial Differential Equations. Lecture Notes in Mathematics, vol 1324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0100794

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  • DOI: https://doi.org/10.1007/BFb0100794

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50111-4

  • Online ISBN: 978-3-540-45928-6

  • eBook Packages: Springer Book Archive

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